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      Solve problems with two unknowns in a range of contexts

      Lesson details

      Learning outcome

      I can solve problems with two unknowns in a range of contexts.

      Key learning points

      1. Some problems with two unknowns have only one solution.
      2. Some problems with two unknowns have many solutions.
      3. Some problems with two unknowns have an infinite number of solutions.

      Keywords

      • Represent - To represent something means to show something in a different way.

      Common misconception

      When representing problems with more than two unknowns, pupils draw bar models all starting from the same end point and with the variables in any order.

      Encourage pupils to draw their bar models with the variables lined up underneath one another wherever possible. The bar model may not line up form the left, but this can help to identify the differences between each model.

      Teacher tip

      Once the bar models have been drawn, ask pupils to notice 'what is the same?' and 'what is different?' between each set. Pupils can represent the difference in bar lengths using an arrow and annotate representations to do this accordingly.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      1 apple and 2 bananas cost £1.85 3 apples and 2 bananas cost £2.75 Complete the equations to represent this. a + 2b = £1.85 and + 2b = £2.75

      Correct Answer: 3a

      Q2.
      Which pair of equations represent the image?

      An image in a quiz
      Correct answer: 3s + l = 100 and 2s + l = 80
      ss + l = 100 and 3s + l = 80
      s + l = 100 and s + l = 80

      Q3.
      Match the mass in kilograms to its equivalent mass in grams.

      Correct Answer:1.205 kg,1,205 g

      1,205 g

      Correct Answer:1.25 kg,1,250 g

      1,250 g

      Correct Answer:1.025 kg,1,025 g

      1,025 g

      Q4.
      £10 is shared between 8 people. How much does each person get? Write your answer in pounds. £

      Correct Answer: 1.25, £1.25

      Q5.
      If four peaches cost £3.40, what is the cost of one peach? Give your answer in pence. p

      Correct Answer: 85, 85 pence, 85 p

      Q6.
      1 apple and 2 bananas cost £1.85 3 apples and 2 bananas cost £2.75 What is the cost of one banana? Give your answer in pence.

      Correct Answer: 70 p, 70, 70 pence

      6 Questions

      Q1.
      1 eraser (a) and 3 pencils (3b) cost £1.75 4 erasers (4a) and 3 pencils (3b) cost £2.50 Which statements are true?

      An image in a quiz
      There is an equal number of erasers.
      Correct answer: There is an equal number of pencils.
      Correct answer: The difference in cost is equal to 3 erasers.
      The difference in cost is equal to 3 pencils.

      Q2.
      1 eraser (a) and 3 pencils (3b) cost £1.75 4 erasers (4a) and 3 pencils (3b) cost £2.50 Find the cost of one eraser. p

      An image in a quiz
      Correct Answer: 25, 25 p, 25 pence

      Q3.
      The masses of some groups of large and small bags of potatoes are shown here. What is the mass of the large bag? kg

      An image in a quiz
      Correct Answer: 2.6, 2.6 kg

      Q4.
      Two different designs are made with the same square and triangular tiles. The area of the whole design is given. What is the area of one triangular tile? $$cm^2$$

      An image in a quiz
      Correct Answer: 9

      Q5.
      Lucas knows that the cost of 1 lemon is 30 p. What is the missing total highlighted? Give your answer in pounds. £

      An image in a quiz
      Correct Answer: 1.10, £1.10

      Q6.
      Lucas knows that the cost of 1 lemon is 30 p and the cost of 1 pear is 50 p. What is the missing total highlighted? Give your answer in pounds. £

      An image in a quiz
      Correct Answer: 1.30, £1.30

      To help you plan your 6 maths lesson on: Solve problems with two unknowns in a range of contexts, download all teaching resources for free and adapt to suit your pupils' needs...